Problem: Simplify the following expression: $k = \dfrac{q^2 + 10q + 21}{q + 7} $
First factor the polynomial in the numerator. $ q^2 + 10q + 21 = (q + 7)(q + 3) $ So we can rewrite the expression as: $k = \dfrac{(q + 7)(q + 3)}{q + 7} $ We can divide the numerator and denominator by $(q + 7)$ on condition that $q \neq -7$ Therefore $k = q + 3; q \neq -7$